In　this　paper,　we　studies　consensus　problems　for　double-integrator　multi-agent　systems　subject　to　external　disturbances　and　randomly　switching　topologies　which　obeys　time　homogeneous　Markov　process.　Building　on　the　tenets　of　the　stochastic　stability　theory　and　the　H∞　control　approach,　the　sufficient　condition　of　consensus　with　H∞　performance　is　derived　for　the　systems.　The　control　protocol　presented　is　a　common　one　which　is　not　strictly　dependent　on　random　state.　Finally,　the　theoretical　results　were　verified　by　simulation.　©　2019　IEEE.